By E. Robert Fernholz
1. Stochastic Portfolio concept --
2. inventory marketplace habit and variety --
3. Functionally Generated Portfolios --
4. Portfolios of shares chosen through Rank --
5. sturdy versions for the Distribution of Capital --
6. functionality of Functionally Generated Portfolios --
7. functions of Stochastic Portfolio idea --
App. A. review of neighborhood occasions.
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Additional info for Stochastic portfolio theory
5. The weights 7ri(t) sum to 1, and the conditions on S ensure that 7r is a portfolio. 8) that 8 is of bounded variation. 9) n L Dij log S(/L(t))/Li(t)/Lj(thj (t) dt. , for t E [O,Tj. L(t)) must be equal. 4. 7) is satisfied. Li(t) = 0. L(t)) are equal. 48 3. 2. , for t E [O,T], n i=l 1 n - "2 L i,j=l Ddog S(JL(t) )Dj log S(JL(t) )JLi(t)JLj (thj (t) dt. 8) is proved. 6 Example. Here are a few examples of simple generating functions and the portfolios they generate. 1. S(x) = 1 generates the market portfolio JL with 8(t) = 0.
2: The market portfolio fJ is defined by the market weights fJl, ... 9) for i = I, ... ,n. The market portfolio is the canonical performance benchmark for all other portfolios. The value Zp of the market portfolio satisfies Zp(t) = Xl(t) + ... , for i = 1, ... , n. , for t E [0,(0). Hence, we can analyze the relative portfolio performance in terms of the changing market weights and the excess growth rate, so it will be important for us to develop an understanding of the behavior of both the market weights and the excess growth rate.
N and for all x E Don if and only if 8d8 2 is constant on Don.